1. Field of the Invention
The present invention generally relates to a method and system to embed an image. More particularly, the present invention relates to a method and system to embed one or more images into two or more other images.
2. Description of the Related Art
Recently, several watermarking schemes have been proposed where a watermark is embedded in two halftone images such that the watermark can be extracted by simply overlaying these halftone images.
In one conventional method, the two halftone images are created using dither masks, while another conventional method creates the two halftone images using an error diffusion technique. The watermark images in these schemes are binary images and any correlation between the binary pixels of the two halftone images depends upon whether corresponding pixels in the watermark are black or white.
There are several limitations to these conventional methods of extracting watermarks. First, the watermark images must be binary and cannot be grayscale or color.
Second, because the watermark is embedded in the two images based upon a correlation, the average intensity of a region of pixels is needed to identify whether the watermark pixel is black or white. Therefore, the watermark images that may be extracted using these conventional methods may only be simple graphics. In other words, the watermarks are limited to simple images such as logos or simple graphics and cannot contain detailed features.
Third, the watermark images that are extracted using these conventional methods contain residual patterns and features from the two halftone images in which the watermark was embedded. These residual patterns and features reduce the fidelity of the watermark image that is extracted. Therefore, this is another reason why a watermark image cannot have fine details and be successfully processed using a conventional watermarking method.
Fourth, the embedding by these conventional methods is only capable of generating binary halftone images, rather than grayscale or multi-bit images. These binary halftone images also limit the fidelity of the extracted watermark.
Consider an image as a matrix of pixels, i.e. an image G includes pixels G(i,j) where G(i,j), the (i,j)-th pixel of image G, is a vector in a color space. For grayscale pixels, the color space may be one-dimensional whereas for RGB pixels, the color space may be 3-dimensional. A set of n images G1, G2, . . . , Gn of the same size can be considered as a matrix of n-tuples of pixels. This is denoted as G1×G2× . . . ×Gn, i.e. the (i,j)-th element of G1×G2× . . . ×Gn is the n-tuple (G1(i,j), . . . , Gn(i,j)). Equivalently, a set of n images can be considered as a single image whose color space is the Cartesian product of the n color spaces of the images G1, G2, . . . , Gn.
Consider an image transform “Φ” which acts on an n-tuple of pixels and produces an m-tuple of pixels, i.e. Φ(p1, . . . , pn)=(q1, . . ., qm) where pi and qi are pixels. By applying the transform Φ to each of the n-tuples of pixels in G1×G2× . . . ×Gn, this transform acts on a set of n images and produces m images. The m auxiliary images may be watermark images that are extracted by the watermark extraction transform Φ.
Another aspect to consider is how images are perceived under different viewing conditions. In other words, the n images plus the m extracted images can be considered as how a single image is perceived under different viewing conditions. Such an interpretation for the case n=1 can be found in C. W. Wu et al, “Multiple images viewable on twisted-nematic mode liquid-crystal displays,” IEEE Signal Processing Letters, vol. 10, no. 8, pp. 225-227, 2003.
If a goal is to produce a set of n images, such that these images plus the additional m images that are generated by the transform Φ matches another set of n+m predefined images, perfect matching is not possible because there are more sets of n+m images than there are sets of n images.
Instead of perfect matching, conventional watermarking methods utilizing halftoning take advantage of the fact that the images only need to look similar when viewed at an appropriate distance. Because of the “low pass behavior” of the human vision system, only low-pass versions of the images need to match. In this manner, the human visual system reduces the amount of information in images, which allows the use of a digital half-toning algorithm to provide a solution to the problem.
Yet another conventional watermarking scheme constructs two binary halftone images A and B, which when overlaid on top of each other reveals a watermark image C. Assuming that each pixel of image A and image B are either 0 (denoting a white pixel) or 1 (denoting a black pixel), the overlay operation can be expressed as C(i,j)=A(i,j)ΘB(i,j) where function “Θ” is the OR operation.
These conventional methods embed the watermark image based on a correlation of the pixels between the two images and the ability to extract a watermark is based upon whether corresponding pixels in each of the two images vary together. For example, for a watermark image W that is a binary image, when W(i,j)=0, the corresponding pixels in A and B are correlated and when W(i,j)≠0 the corresponding pixels in A and B are not correlated. This implies that when W(i,j)=1 the overlaid pixels C(i,j) will be darker on average than when W(i,j)=0 and, thus, C will reveal the watermark image W. However, as explained above, the pixels that are not correlated are darker than the correlated pixels only when averaged over a region of pixels. Therefore, the watermark cannot contain fine details. Furthermore, the pixels in the watermark image still reveal residual features of images A and B when overlaid.